Simplify the following expression: $a = \dfrac{-99y^3 - 66y^2}{-121y^2}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-99y^3 - 66y^2 = - (3\cdot3\cdot11 \cdot y \cdot y \cdot y) - (2\cdot3\cdot11 \cdot y \cdot y)$ The denominator can be factored: $-121y^2 = - (11\cdot11 \cdot y \cdot y)$ The greatest common factor of all the terms is $11y^2$ Factoring out $11y^2$ gives us: $a = \dfrac{(11y^2)(-9y - 6)}{(11y^2)(-11)}$ Dividing both the numerator and denominator by $11y^2$ gives: $a = \dfrac{-9y - 6}{-11}$